Design, development and validation of electron ionisation models for nano -scale simulation

1. Design, development and validation of electron ionisation models for nano-scale simulation HeeSeo, Chan-Hyeung Kim, Lorenzo Moneta, Maria GraziaPia Hanyang Univ. (Korea), INFN Genova (Italy), CERN (Switzerland) 18 October 2010 SNA + MC 2010 Joint International Conference on Supercomputing in Nuclear Applications + Monte Carlo 2010

2. Outline • Experimental and software context • Electron ionisation cross section models • Software development and verification • Experimental validation • Conclusions and outlook

3. Experimental requirements • Nano-scale simulation is required in various experimental applications: • Nanotechnology-based radiation detectors • Radiation effects on semiconductor devices • Gaseous tracking detectors • Plasma physics including material processes • Biological effects of radiation • etc. HEP detector R&D LHC and beyond Radiation protection

4. Monte Carlo codes • General-purpose Monte Carlo simulation codes • Geant4, MCNP, EGS etc. • based on condensed history technique • cutoff energy / secondary production threshold: 1 keV • Penelope, Geant4 low energy models • < 1 keV, butscarce quantitative evidence of modeling accuracy below 1 keV • Conventional particle transport scheme and physics models are adequate for macroscopic observables; however, they are NOT appropriate for nano-scale simulation • “Track structure codes” • Developed ad hoc for nano-scale simulation • Limited applicability: usually specific to one or a few materials • Limited public availability • Long term maintenance is often an issue

5. Vision For the first time, endow a general purpose Monte Carlo code with the capability of nano-scale simulation for any material Further advancement: multi-scale simulation in the same software environment seamless transition between particle transport schemes 1stdevelopment cycle: focused on electron impact ionisation the very heart of the problem! Cross sections this talk Final state generator in progress Major investment in the experimental validation of the new physics models Also: for the first time, validation of EEDL below 1 keV

6. Development strategy • Cross section models for electron impact ionization at energies down to the ionization potential (a few eV) for any target atom: • implemented (based on existing design) • verified, • validated • Cross section models: • Binary-Encounter-Bethe (BEB) • Deutsch-Märk(DM) • EEDL

7. Ionisation cross sections: BEB model • Binary-Encounter-Bethe (BEB) model • Proposed by Kim and Rudd in 19941 • Simplified version of BED (Binary Encounter Dipole) model • Modified form of Mott theory for close collision • Dipole interaction of Bethe theory for distant collision • Total ionization cross section • In the present study, orbital parameters (Bk, Uk, Nk) in EADL2 were used B=binding energy U=<kinetic energy> N=occupation number of shell 1. Y. Kim and M. Rudd, Phys. Rev. A 50(5):3954–3966 (1994). 2. S. T. Perkins et al., UCRL-50400, vol.30 (1991).

8. Ionisation cross sections: DM model • Deutsch-Märk (DM)1 model • Originated from Thomson2 and Gryzinski3 • Some parameters are derived from fits to experimental data • Values of these fitted parameters are reported in original author’s publications • The up-to-date formula is • H. Deutsch, T. D. Märk, Int. J. Mass Spectrom. Ion Processes, 79:R1–R8 (1987). • J. J. Thomson, Philos. Mag., 23:449–457 (1912). • M. Gryzinski, Phys. Rev. A, 138:305–321 (1965).

9. Ionisation cross sections: EEDL • Evaluated Electron Data Library (EEDL)1 • Lawrence Livermore National Laboratory (LLNL) • Z=1–100 and E=10 eV–100 GeV • Elastic scattering, Bremsstrahlung, excitation and impact ionization cross sections • Ionization cross sections for each shell (i.e., K, L, M, …) • Based on Seltzer’s modifications on • Möller binary collision cross section for close collisions • Weizsacker-Williams method for distant collisions 1. S. T. Perkins et al., UCRL-50400, vol.31 (1991)

10. Cross sections of the three models Large differences for some elements Similar values for some elements

11. Software design • Policy-based class design • See: M.G. Pia et al., Design and performance evaluations of generic programming techniques in a R&D prototype of Geant4 physics , CHEP 2009 • Main advantages: • fine-grained configuration of particle interaction processes with a variety of physics models • computational performance • ease of test (verification and validation) • Prototype design • Subject to further refinement based on concrete experience and experiments’ feedback

12. Implementation • The implementation was based on the most recent formulations and associated parameters of the BEB and DM models • The atomic parameters needed by the models’ formulation were taken from the same sources as the original authors’ ones whenever practically possible • If not available, they were taken from EADL or NIST • Side project: validation of some atomic parameters used by major Monte Carlo systems (paper in preparation) • Based on this implementation, the electron ionization cross section can be calculated for Z=1-100 and energies from the ionization potential up to10 keV

13. Verification • Verification was done by comparing calculated values to published data by original authors • 48 atoms for DM model, 8 atoms for BEB model • In most cases, they show good agreement • differences associated with different atomic parameters DM model for oxygen (Z=8) atom BEB model for boron (Z=5) atom

14. Validation • Experimental data used in the validation process • 181 experimental data sets for 57 atoms Elements for which experimental data are available

15. Validation: sometimes it is easy… H (Z=1) He (Z=2) Ne (Z=10) Several independent measurements, mostly compatible among them Ar (Z=18) Kr (Z=36)

16. Validation: who is right? Na (Z=11) Mg (Z=12) Ga (Z=31) Several independent measurements, mostly incompatible among them Eu (Z=63) Cs (Z=55)

17. Validation: shall we trust a single measurement? Cl (Z=17) Si (Z=14) C (Z=6) Limited availability of experimental data (some not documenting errors) Au (Z=79) Cd (Z=48) Ti (Z=22)

18. Validation method • Validation process exploited rigorous statistical analysis to quantitatively estimate the compatibility with experimental data for the two theoretical models as well as EEDL • Validation process divided into two parts: • Goodness-of-fit tests to evaluate the hypothesis of compatibility between calculated values and experimental data • Categorical analysis exploiting contingency tables using Fisher’s exact test, χ2 test with Yates correction, and Pearson χ2 test • Validation tests were performed in various energy ranges <20 eV, 20–50 eV, 50–100 eV, 100–250 eV, 250 eV–1 keV, >1 keV • Possible sources of systematic effects evaluated • Single vs. totalionisation, absolute vs. relative measurement

19. Validation results Percentage of elements for which a model is compatible with experimental data at 95% CL • GoF tests • c2 • Kolmogorov-Smirnov • Anderson-Darling • Cramer-von Mises DM model best overall accuracy EEDL degradedaccuracy below 250 eV

20. Detailed results Percentage of test cases in which cross section models are compatible with experimental data Preliminary

21. Significance of DM-BEB differences Contingency tables related to DM and BEB cross section compatibility with experimental data Preliminary

22. Significance of DM-EEDL differences Contingency tables related to DM and EEDL cross section compatibility with experimental data Preliminary

23. Conclusions Paper with full set of results in progress • Electron ionization cross section models suitable for nano-scale simulation are available for use with general purpose Geant4 • Capability for the first time available in a Monte Carlo system • Rigorous validation w.r.t. extensive collection of independent experimental measurements • We demonstrated that • DM model shows the best agreement with experiment • BEB model’s accuracyis comparable to DM model’s for E up to 50 eV and above 250 eV, worse for 50 < E < 250 eV • EEDLshows lower accuracy below 250 eV • Outlook • New cross section models will be proposed for release in the Geant4 toolkit • Cross section data will be distributed as a data library (RSICC at ORNL) • Final state generator development in progress • Generic host ionization process is already available • Extensions to molecules and other refinements are foreseen